NuSTAR AND XMM-NEWTON OBSERVATIONS OF THE HARD X-RAY SPECTRUM OF CENTAURUS A

NuSTAR consists of two independent grazing incidence telescopes, focusing X-rays between 3 and 78 keV on corresponding focal planes consisting of cadmium–zinc–telluride pixel detectors. NuSTAR provides unprecedented sensitivity and high spectral resolution at energies above 10 keV, ideally suited to studying the Compton reflection hump. The two focal planes are referred to as focal plane modules (FPM) A and B. NuSTAR data were extracted using the standard NUSTARDAS v1.3.1 software. Source spectra were taken from a 100'' radius region center on the J2000 coordinates. The background was extracted as far away from the source as possible, from a 120'' radius region. This approach induces small systematic uncertainties in the background, as the background is known to change over the field of view (Wik et al. 2014). However, Cen A is over a factor ∼10 brighter than the background even at the highest energies, so that these uncertainties are negligible. NuSTAR data were binned to a signal-to-noise ratio (S/N) of 20 in the relevant energy range of 3–78 keV within ISIS.

The average count-rate during the observations was ≈18.5 cts s⁻¹ per module. Only very slight variability was evident, with the count-rate declining by about 5% over the observation. No changes in hardness were visible, so we use the time-averaged spectrum for the remainder of this paper.

XMM-Newton observed Cen A as part of the Tracking Active Galactic Nuclei with Austral Milliarcsecond Interferometry program (TANAMI), an ongoing multi-wavelength, multi-year monitoring program of southern AGNs (Ojha et al. 2010; Müller et al. 2014). We reduced the XMM-Newton data using the standard scientific analysis software version xmmsas_20141104_1833-14.0.0+. The EPIC-pn camera (Strüder et al. 2001) was operated in small window mode to alleviate pile-up, while the MOS cameras (Turner et al. 2001) were operated in full frame mode to obtain a measurement of the diffuse and jet components. A detailed analysis of the XMM-Newton data will be presented in a forthcoming publication (C. Müller et al. 2016, in preparation). Here we concentrate on the energy range >3 keV for a direct comparison with the NuSTAR data and to avoid contamination from the soft X-ray emission from the thermal extended plasma and the off-nuclear point sources.

Even though EPIC-pn was operated in the small window mode, the count-rate of ≈30 cts s⁻¹ is enough to cause pile-up (see the XMM-Newton users' handbook issue 2.13).¹⁹ We therefore carefully analyzed extraction regions with different annuli and compared spectral shapes and the results from epatplot. We found that only negligible fractions of pile-up remain for an inner radius of 10''. We set the outer radius to 40'', the largest radius possible with the region fully on the chip, as the source was located close to the north–east border of the chip. We rebinned the pn data to a S/N of 15 between 3 and 10 keV.

Having been operated in full window mode, MOS 1 and 2 were more significantly piled-up, and we excluded the inner 20'' to remove most pile-up effects. We set the outer radius to 100'' to be comparable to the NuSTAR extraction region and rebinned the spectra to an S/N of 11.5 between 3 and 9 keV to retain sufficient spectral resolution for line spectroscopy despite the lower effective area compared to pn. Within that annulus, no other point source is visible. A more detailed study of the jet spectrum including Chandra will be presented in a forthcoming publication (C. Graefe et al. 2016, in preparation).

All annuli were centered on the J2000 coordinates of Cen A. The XMM-Newton data were taken contemporaneously to NuSTAR, overlapping in the last part of the longer NuSTAR observation. The complete observation log is given in Table 1.

We first fit the data with an absorbed power law as shown in Figure 2. A prominent $\mathrm{Fe}\;{\rm{K}}\alpha$ line is visible in the residuals (Figure 2(b)), which can be described with a narrow Gaussian around 6.4 keV with an equivalent width of $\approx 40\;{\rm{eV}}$. The Gaussian is narrower than the energy resolution of XMM-Newton and we only find upper limits for its width. The absorption is modeled with the phabs model, using abundances by Wilms et al. (2000) and cross-sections by Verner et al. (1996). This model gives a good fit (${\chi }_{\mathrm{red}}^{2}$ = 1.04 for 1532 degrees of freedom (dof)) with a power-law index Γ = 1.815 ± 0.005. We calculate an unabsorbed 3–50 keV luminosity of $\approx 3.4\times {10}^{42}$ erg s⁻¹. All parameters can be found in Table 2. Note that uncertainties are purely statistical and do not take systematic differences between the detectors into account (e.g., the photon index can vary by $\approx 0.01$ between consecutive observations in NuSTAR and the line energies have about 15 eV systematic uncertainties; see Madsen et al. 2015b).

Table 2.  Model Parameters for the Simultaneous NuSTAR and XMM Spectra

Parameter	Power Law	Cutoff-PL	pexrav	compPS	MYtorus	BNtorus
NH (1022 cm−2)	${17.06}_{-0.24}^{+0.26}$	16.78 ± 0.26	${16.79}_{-0.25}^{+0.26}$	${16.86}_{-0.31}^{+0.30}$	${11.00}_{-0.20}^{+1.53}$	${9.92}_{-0.25}^{+0.14}$
${{ \mathcal F }}_{\mathrm{cont}}$ a	0.9946 ± 0.0024	0.9896 ± 0.0024	0.9918 ± 0.0024	${0.9936}_{-0.0024}^{+0.0028}$	⋯	⋯
Γ	1.815 ± 0.005	1.797 ± 0.005	1.797 ± 0.005	⋯	1.824 ± 0.006	${1.826}_{-0.008}^{+0.009}$
${E}_{\mathrm{fold}}\;\mathrm{or}\;{kT}\;(\mathrm{keV})$	⋯	$({1.000}_{-0.075}^{+0.000})\times {10}^{3}$	$({1.000}_{-0.054}^{+0.000})\times {10}^{3}$	$({2.16}_{-0.22}^{+0.19})\times {10}^{2}$	⋯	⋯
R	⋯	⋯	$\leqslant 0.011$	$\leqslant 0.012$	⋯	⋯
y	⋯	⋯	⋯	0.402 ± 0.016	⋯	⋯
$i\;[\mathrm{deg}]$	⋯	⋯	60 (fix)	60 (fix)	>75.8	${63.30}_{-0.11}^{+4.29}$
${{\rm{\Theta }}}_{\mathrm{tor}}\;(\mathrm{deg})$	⋯	⋯	⋯	⋯	60 (fix)	${60.00}_{-2.97}^{+0.13}$
${I}_{\mathrm{Fe}}$ b	$(2.76\pm 0.22)\times {10}^{-4}$	$(2.88\pm 0.22)\times {10}^{-4}$	$(2.86\pm 0.22)\times {10}^{-4}$	$(3.38\pm 0.26)\times {10}^{-4}$	⋯	⋯
EFe (keV)	${6.404}_{-0.009}^{+0.005}$	${6.404}_{-0.008}^{+0.004}$	${6.402}_{-0.006}^{+0.007}$	${6.404}_{-0.007}^{+0.004}$	⋯	⋯
σFe (eV)	$\leqslant 8.7$	$\leqslant 8.8$	$\leqslant 8.5$	$\leqslant 8.7$	⋯	⋯
${\mathrm{CC}}_{\mathrm{FPMB}}$	1.0366 ± 0.0028	1.0366 ± 0.0028	${1.0366}_{-0.0026}^{+0.0028}$	1.0366 ± 0.0028	1.032 ± 0.004	1.032 ± 0.004
${\mathrm{CC}}_{\mathrm{pn}}$	0.848 ± 0.007	0.847 ± 0.007	0.847 ± 0.007	0.847 ± 0.007	0.866 ± 0.009	0.869 ± 0.009
${\mathrm{CC}}_{\mathrm{MOS}1}$	1.214 ± 0.016	1.212 ± 0.016	1.212 ± 0.016	${1.213}_{-0.014}^{+0.016}$	${1.109}_{-0.018}^{+0.019}$	${1.116}_{-0.018}^{+0.019}$
${\mathrm{CC}}_{\mathrm{MOS}2}$	1.238 ± 0.016	1.236 ± 0.016	1.237 ± 0.016	${1.237}_{-0.015}^{+0.016}$	1.128 ± 0.019	1.135 ± 0.019
${\chi }^{2}/\mathrm{dof}$	1595.50/1532	1620.63/1531	1620.67/1530	1595.72/1531	1667.04/1536	1695.77/1535
${\chi }_{\mathrm{red}}^{2}$	1.041	1.059	1.059	1.042	1.085	1.105

Notes.

^aUnabsorbed flux in keV s⁻¹ cm⁻² [3–50 keV]. ^bIn ph s⁻¹ cm⁻².

Download table as:  ASCIITypeset image

To investigate the process responsible for the hard X-ray continuum and estimate the coronal temperature in a thermal Comptonization scenario, we searched for the presence of an exponential rollover at high energies by replacing the power law with the cutoffpl model in XSPEC. The fit did not improve and we obtained a lower limit of ${E}_{\mathrm{fold}}\gt 1\;{\rm{MeV}}$ (see Table 2). This limit is far above the NuSTAR energy range and therefore unreliable. However, as the cutoffpl is only a phenomenological model that shows continuous curvature even far below the folding energy, this result indicates that the 3–78 keV spectrum of Cen A is a pure power law.

For a more realistic description of a continuum produced by Comptonization, we applied the compps model (Poutanen & Svensson 1996). Following Beckmann et al. (2011), we assume a multi-colored disk with a slab geometry and fit for the Compton-y parameter. The disk input temperature cannot be constrained with our data due to obscuration, so in a first approach we fix it at ${{kT}}_{\mathrm{BB}}$ = 10 eV, appropriate for a black hole mass of 5 × 10⁷ ${M}_{\odot }$ accreting at very low Eddington fractions (Makishima et al. 2000). The compps model also includes a reflection component based on the pexrav model and described by the reflection strength R, which we allow to vary. The inclination²⁰ was set to $i=60^\circ$. To describe the $\mathrm{Fe}\;{\rm{K}}\alpha$ line, we added a Gaussian component and obtained a very good fit, with ${\chi }_{\mathrm{red}}^{2}=1.04$ for 1531 dof. The values obtained for $y=0.402\pm 0.016$ and the coronal temperature ${{kT}}_{e}={216}_{-22}^{+19}$ keV agree very well with the results from Beckmann et al. (2011); see Table 2. We only find an upper limit on the reflection strength at the 90% confidence level of $R\leqslant 0.012$.

We investigated the influence of the disk input temperature on other parameters within a reasonably expected range, sampling temperatures between ${{kT}}_{{\mathtt{BB}}}$ = 5–50 eV. We find that the plasma temperature to first order decreases with hotter disk temperatures, from ${277}_{-26}^{+21}$ keV at 5 eV to ${118}_{-14}^{+13}$ keV at 50 eV. At higher input temperatures, however, a secondary minimum evolves at high plasma temperatures around 350 keV, which becomes statistically preferred above ∼60 eV. At ${{kT}}_{{\mathtt{BB}}}=100\;{\rm{eV}}$ we then measure an electron temperature of ${304}_{-16}^{+19}$ keV. We note that a disk temperature above 50 eV is likely too high for the parameters of Cen A's black hole and we therefore do not investigate this solution further.

Using the comptt model (Titarchuk 1994) only gives a lower limit of ${{kT}}_{e}\gt 475\;{\rm{keV}}$. The measured value of the electron temperature should be taken with a grain of salt and is strongly influenced by our assumptions. A full investigation of the systematic uncertainties is, however, beyond the scope of this paper.

Despite the fact that electron temperature is above the energy range covered by NuSTAR, we can constrain kT_e for a given disk temperature due to the spectral shape and the high S/N of our data. In Figure 3 we show the χ² confidence contours for kT_e versus the Compton-y parameter, assuming ${{kT}}_{\mathrm{BB}}=10\;{\rm{eV}}$. While a clear degeneracy can be seen, both parameters are well constrained. When we directly fit for the optical depth τ instead of y, we find a very similar contour and a best-fit value of $\tau ={0.240}_{-0.027}^{+0.041}$.

Zoom In Zoom Out Reset image size

To test if the intrinsic shape of the compps is concealing any weak reflection component, we then modeled the spectrum using only the pexrav model. We note that the pexrav model does not make any assumptions about the geometry of the reflecting medium and is therefore also mostly a phenomenological model to test for the presence of curvature. Again, we only obtain an upper limit of $R\leqslant 0.010$ on the reflection fraction (Table 2). The value depends on the assumed inclination (here we used an inclination of $i=60^\circ$ following Fukazawa et al. 2011) and is even lower for smaller angles ($\approx 0.006$ at the model maximum $\mathrm{cos}(i)=0.95$). This limit is similar to the one obtained by Rivers et al. (2011b) using RXTE data ($R\lt 0.005$).

Models that self-consistently describe the reflection spectrum off an optically thick disk, like pexmon (Nandra et al. 2007), reflionx (Ross & Fabian 2007), and xillver (García & Kallman 2010), and include line fluorescence and a Compton hump, fail to provide an adequate description of the spectrum within physically sensible parameters. These models cannot combine the strength of the iron line with the lack of a Compton hump, indicating that the $\mathrm{Fe}\;{\rm{K}}\alpha$ line does not originate from reflection off Compton-thick material.

Finally, we tested physically motivated models for the presence of a toroidal obscuring structure in the nuclear region of Cen A. We applied the X-ray spectral models of Brightman & Nandra (2011, BNTorus) and Murphy & Yaqoob (2009, MYTorus), which were designed specifically for this purpose. The models self-consistently account for photoelectric absorption, fluorescence line emission (most importantly from $\mathrm{Fe}\;{\rm{K}}\alpha$), and Compton scattering, assuming a toroidal geometry. The MYTorus model assumes an obscuring torus with a circular cross-section and a fixed opening angle ${{\rm{\Theta }}}_{\mathrm{tor}}$ of 60°, while the BNTorus model assumes a spherical torus where ${N}_{{\rm{H}}}$ is independent of the inclination (i.e., viewing angle) i. The spherical torus is modified by a biconical void with a variable opening angle ${{\rm{\Theta }}}_{\mathrm{tor}}$. Furthermore, BNTorus allows for variation of the covering factor of the torus, whereas MYTorus has a fixed covering factor of 0.5. For a recent comparison between these two models, see Brightman et al. (2015).

The BNTorus and MYTorus models measure similar line-of-sight column densities, ${N}_{{\rm{H}}}={9.92}_{-0.25}^{+0.13}\times {10}^{22}$ cm⁻² and ${11.00}_{-0.20}^{+1.53}\times {10}^{22}$ cm⁻², respectively. The lower column densities compared to the previous models are due to the fact that the torus models also include Compton scattering, while phabs does not, which leads to an overestimation of the column in the latter. This is also reflected in the slightly lower unabsorbed 3–50 keV luminosity of the BNTorus model of $\approx 3.1\times {10}^{42}$ erg s⁻¹. The opening angle of the torus measured by BNTorus is ${60.00}_{-2.97}^{+0.13}$ degrees, which corresponds to a covering factor of 0.5. This covering factor compares well to other local AGNs of similar luminosity, such as NGC 1068, NGC 1320, and IC 2560 (Baloković et al. 2014; Bauer et al. 2015; Brightman et al. 2015).

For MYTorus, the inclination angle of the torus is derived to be $\geqslant 76$°. MYTorus has the added flexibility of decoupling the scattered and fluorescent line components from the transmitted component in order to test for scattering out of the line of sight. However, when allowing for such a decoupling we only find marginal improvement in terms of ${\chi }^{2}$ and the inclination angle becomes completely unconstrained. In that case we can place an upper limit of $1.15\times {10}^{23}$ cm⁻² on the ${N}_{{\rm{H}}}$ of any material out of the line of sight, consistent with what is seen along the line of sight.

Using Suzaku XIS and GSO data, Fukazawa et al. (2011) found a significant reflection fraction of the order of $R\approx 0.2$. Their best-fit model includes two power-law components describing the AGN core emission and the jet contribution separately. When applying their model to the XMM-Newton and NuSTAR data we cannot confirm such high reflection fractions but instead obtain upper limits on R similar to those in the simpler models presented in Table 2. Following Fukazawa et al. (2011) and using the pexmon model to self-consistently describe the $\mathrm{Fe}\;{\rm{K}}\alpha$ line and fixing the photon indices at 1.6 and 1.9, respectively, we obtain R = 0.138 ± 0.016. However, the fit is clearly worse than the fits with only a single power law (${\chi }_{\mathrm{red}}^{2}=1.16$ for 1531 dof).

We also investigated the presence of a partial covering model for the primary absorber, as used by, e.g., Evans et al. (2004). Because we only consider data above 3 keV, our limits are only marginally constraining, and we find a covering fraction $\gt 0.98$. In Section 4.2 we extend the energy range down to 2 keV and find weak evidence for partial covering.

Using Suzaku data, Tombesi et al. (2014) found evidence for two weak absorption lines at 6.66 and 6.95 keV, which they interpreted as evidence for a slow wind. Similar absorption lines have recently been discovered in the NuSTAR spectrum of Cyg A, a bright FRII galaxy (Reynolds et al. 2015). When adding Gaussian absorption lines to our data of Cen A, with the energies fixed at the values found by Tombesi et al. (2014) and the width set to 1 eV, we find a marginal improvement of ${\rm{\Delta }}{\chi }^{2}=7$ for two additional parameters. However, if we allow the energies to vary, the fit does not converge. The failure to detect significant absorption features could be due to the much lower S/N in the XMM-Newton data compared to the Suzaku data used by Tombesi et al. (2014). We therefore do not include these lines in our discussion.

In the preceding section we attributed differences between the XMM-Newton and NuSTAR spectra to pile-up and cross-calibration differences. The strength of these effects required to explain the differences is, while not impossible, somewhat surprising. We therefore made an effort to rule out astrophysical or source intrinsic effects that could cause this discrepancy. The main source of intrinsic background contributing to the measured spectrum is diffuse emission surrounding the AGN as seen with Chandra. Due to the different PSF sizes of XMM-Newton and NuSTAR, the instruments sample different amounts of this diffuse emission, which might influence the observed spectral slope.

To check the influence of the diffuse emission as a function of distance to the AGN, we extracted spectra in different annuli from the XMM-Newton cameras. For the pn camera we use rings with 5''–15'', 15''–25'', and 25''–40''. We chose to avoid the central 5'' to ensure the innermost pixel is excluded given pn's pixel size of 41. For MOS 1 and 2 we use annuli with 15''–20'', 20''–40'', 40''–60'', 60''–80'', and 80''–100''.

For NuSTAR we used an extraction region of 100'', as described in Section 2.1. We also extracted spectra from smaller regions (10'' and 40'') but did not find a significant difference in the spectral shape. We therefore chose to use the largest region for the best S/N.

We then fitted all these spectra simultaneously using a absorbed power law plus a Gaussian iron line. We required that all data have the same absorption column, photon index, and iron line energy, i.e., only allowed for the normalization of the continuum and the line to be different between the data sets. The iron line width was fixed to 10⁻⁶ keV, far below the energy resolution of any of the instruments.

Zoom In Zoom Out Reset image size

When restricting the energy range to 5–78 keV for NuSTAR and 3–10 keV for XMM-Newton, we obtain a fit with values similar to those of the power-law fit in Table 2 (model A; see Table 3 in the Appendix), but with a worse statistical quality (${\chi }_{\mathrm{red}}^{2}=1.38$ for 1699 dof). When extending the energy range for NuSTAR down to 3 keV and for XMM-Newton down to 2 keV we do not find a statistically acceptable fit, even when allowing for a partial covering absorber (${\chi }_{\mathrm{red}}^{2}=2.14$ for 1896 dof). Besides the clear mismatch of NuSTAR between 3 and 5 keV, the strongest residuals are due to the pn data, as shown in Figure 4. These data show different spectral slopes for different extraction region sizes, which might indicate spatial variation of the spectrum due to diffuse emission. This diffuse emission might also influence the NuSTAR spectrum between 3 and 5 keV and could be responsible for the observed discrepancies with XMM-Newton.

Zoom In Zoom Out Reset image size

Table 3.  Model Parameters Using Simultaneous Fits of Different Annuli in XMM

Parameter	Model Aa	Model Bb	Model Cc
NH (1022 cm−2)	17.63 ± 0.22	16.9 ± 0.4	17.8 ± 0.4
${A}_{\mathrm{cont}}$ a	0.2440 ± 0.0027	0.243 ± 0.006	0.253 ± 0.007
CF	⋯	${0.9932}_{-0.0020}^{+0.0022}$	${0.9917}_{-0.0020}^{+0.0021}$
Γ	${1.820}_{-0.004}^{+0.005}$	1.831 ± 0.014	1.852 ± 0.015
Efold (keV)	⋯	⋯	$({1.29}_{-0.14}^{+0.17})\times {10}^{2}$
AFea	$(2.4\pm 0.4)\times {10}^{-4}$	$(2.4\pm 0.4)\times {10}^{-4}$	$(1.8\pm 0.4)\times {10}^{-4}$
${E}_{\mathrm{Fe}}\;(\mathrm{keV})$	${6.4500}_{-0.0185}^{+0.0016}$	${6.408}_{-0.007}^{+0.004}$	${6.407}_{-0.006}^{+0.005}$
BFPM	⋯	0.20 ± 0.09	1 (fix)
Bpn (5''–15'')	⋯	2.75 ± 0.29	${2.76}_{-0.30}^{+0.28}$
Bpn (15''–25'')	⋯	0.5 ± 0.4	${1.36}_{-0.30}^{+0.29}$
Bpn (25''–40'')	⋯	${0.10}_{-0.00}^{+0.12}$	0.60 ± 0.26
BMOS (15''–20'')	⋯	0.44 ± 0.22	0.48 ± 0.22
BMOS (20''–40'')	⋯	0.93 ± 0.29	1.02 ± 0.29
BMOS (40''–60'')	⋯	0.48 ± 0.20	0.53 ± 0.20
BMOS (60''–80'')	⋯	0.87 ± 0.30	0.91 ± 0.30
BMOS (80''–100'')	⋯	${1.0}_{-0.9}^{+9.0}$	${1.0}_{-0.9}^{+9.0}$
${\chi }^{2}/\mathrm{dof}$	2356.72/1699	1989.06/1680	2081.68/1673
${\chi }_{\mathrm{red}}^{2}$	1.387	1.184	1.244

Notes.

^aModel A: power law with measured background.  NuSTAR is between 5 and 79 keV and XMM between 3 and 10 keV. ^bModel B: power law with additional diffuse background with free background scaling factor for all spectra. NuSTAR is between 5 and 79 keV and XMM between 2 and 10 keV. ^cModel C: cutoff power law with additional diffuse background where the background scaling factor for NuSTAR/FPMA is fixed at 1. NuSTAR is between 5 and 79 keV and XMM between 2 and 10 keV.

Download table as:  ASCIITypeset image

To investigate this we simulated how the diffuse emission, as seen with Chandra, influences the background in the different instruments and extraction regions. Details of the simulations are given in the Appendix. From these simulations it becomes clear that the diffuse emission cannot contribute enough flux to alter the observed XMM-Newton and NuSTAR spectra significantly. The core emission dominates over the diffuse background, even at large extraction radii. Even when allowing a scaling factor as a free parameter for each background, we do not obtain a good fit (${\chi }_{\mathrm{red}}^{2}=1.24$ for 1673 dof) and the scaling factors reach unrealistic values (e.g., almost 3 for pn, i.e., the pn background needs to be three times higher than measured with Chandra).

We conclude from this investigation that the observed discrepancies between NuSTAR and XMM-Newton are attributed to pile-up and cross-calibration differences and that the diffuse emission around the AGN does not significantly influence the observed spectra. This result also implies that the measured data are completely dominated by the AGN itself and we obtain a clear view of the hard X-ray emission close to the central engine.

Many radio-loud AGNs that are not pure blazars, have a narrow $\mathrm{Fe}\;{\rm{K}}\alpha$ line with no indication of reflection from a disk close to the black hole and only weak evidence for distant reflection (e.g., 3C 33, Evans et al. 2010; 3C 382, Ballantyne et al. 2014; and 3C 273, Madsen et al. 2015a, see also Woźniak et al. 1998). The lack of relativistically blurred reflection has been discussed extensively in the literature, with the most common explanations being either an ionized inner accretion disk (Ballantyne et al. 2002), a slightly truncated inner accretion disk due to retrograde spin (Garofalo 2009), or an outflowing corona (Malzac et al. 2001, although their model predicts a significantly higher reflection strength for the measured photon index of Cen A). Weak and very weak reflection features are therefore not unusual in radio-loud AGNs like we find for the NuSTAR spectrum of Cen A.

The narrow $\mathrm{Fe}\;{\rm{K}}\alpha$ line likely originates from absorbing material relatively far away from the core. As shown by Rivers et al. (2011a), the absorber in Cen A is not Compton-thick, but is thick enough to produce the observed $\mathrm{Fe}\;{\rm{K}}\alpha$ line strength. In fact, assuming that a spherically symmetric absorbing medium surrounding the X-ray source is responsible for the observed $\mathrm{Fe}\;{\rm{K}}\alpha$ emission, the predicted equivalent width is much higher than observed. Following the calculations of Markowitz et al. (2007), for a measured column density of ${N}_{{\rm{H}}}\quad \approx 1.7\times {10}^{23}$ cm⁻² we obtain ${\mathrm{EW}}_{\mathrm{calc}}=109\;{\rm{eV}}$, compared to $\approx 40\;{\rm{eV}}$ observed. As discussed by Markowitz et al. (2007) a spherically symmetric shell is a very simplified geometry, and if the absorber is only partially covering the X-ray source, the equivalent width will be reduced. Furthermore the calculation assumes solar abundances and the equivalent width can be significantly reduced with a sub-solar iron abundance.

A more realistic absorber geometry is a torus configuration, as invoked for many Compton-thick AGNs and as suggested from the unification scheme (see, e.g., Antonucci 1993). As demonstrated by Matt et al. (2003), column densities around ${N}_{{\rm{H}}}\approx {10}^{23}$ cm⁻² will lead to equivalent widths on the order of 40–50 eV, while not producing any significant Compton hump. As we have shown, physically motivated torus models (MYTorus, BNTorus) describe the data very well and self-consistently explain the strength of the iron line.

Infrared photometry of Cen A can also be well described with a (clumpy) torus model, with the caveat that the contribution of synchrotron emission to the IR data is not known (Ramos Almeida et al. 2009). From these IR models a column density around ${N}_{{\rm{H}}}={6.6}_{-1.8}^{+2.2}\times {10}^{23}$ cm⁻² for the torus is inferred, similar to the absorption column measured in the X-rays.

As shown by Rothschild et al. (2006), using RXTE data taken between 1996 and 2009 and comparing them to previous studies, the flux of the iron line is stable over long timescales (>10 year). We confirm these results and measure ${I}_{\mathrm{Fe}}=(2.76\pm 0.22)\times {10}^{-4}$ ph cm⁻² s⁻¹. Similar values have been seen in Suzaku: ($[2.3\pm 0.1]\times {10}^{-4}$ ph cm⁻² s⁻¹; Markowitz et al. 2007, and [2.7–3.0] × 10⁻⁴ ph cm⁻² s⁻¹; Fukazawa et al. 2011), BeppoSAX (${2.7}_{-1.4}^{+0.8}\times {10}^{-4}$ ph cm⁻² s⁻¹; Grandi et al. 2003), and XMM-Newton ($\approx 2.4\times {10}^{-4}$ ph cm⁻² s⁻¹; Evans et al. 2004).

On the other hand, the continuum flux is strongly variable, by more than a factor of two (e.g., Rothschild et al. 2006). The flux presented here is about 40% higher than the average long-term flux observed by INTEGRAL (averaged over 6 years between 2003 and 2009; Beckmann et al. 2011). This results in a strong variability of the equivalent width of the iron line and limits the applicability of using the instantaneous X-ray flux to calculate the equivalent width. To explain the stability of the $\mathrm{Fe}\;{\rm{K}}\alpha$ flux, the fluorescent region needs to be on the order of 10 ly or more away from the core, to smear out its variations on that timescale. The region can still be much smaller than resolvable even with Chandra (as $1^{\prime\prime}$ is about 55 ly at the distance of Cen A).

Seyfert galaxies produce hard X-rays through thermal Comptonization of soft seed photons in a hot electron-gas corona. The temperature of the corona can be estimated from the energy of the exponential rollover, however, care has to be taken since the cutoffpl model has a distinctly different shape than calculations of a Comptonization spectrum (see, e.g., Petrucci et al. 2001). NuSTAR has measured folding energies in numerous Seyfert galaxies, e.g., IC 4329A (186 ± 14 keV; Brenneman et al. 2014), SWIFT J2127.4+5654 (108 ± 11 keV; Marinucci et al. 2014), MCG−05-23-016 (116 ± 6 keV; Baloković et al. 2015), as well as determined lower limits in NGC 5506 with $\gt 350\;{\rm{keV}}$ and a best-fit $\approx 720\;{\rm{keV}}$ (Matt et al. 2015). Fabian et al. (2015) summarize and discuss these measurements. Recently, NuSTAR observations of the broad-line radio galaxy 3C 390.3 revealed a folding energy of ${117}_{-14}^{+18}$ keV (Lohfink et al. 2015), much lower than we find for Cen A. In Cen A the lower limit is in excess of 1 MeV, which, if the continuum is produced in a thermal corona, indicates a very high plasma temperature.

Following the calculations by Fabian et al. (2015) this very high temperature would put Cen A's corona far above the pair-production line for a coronal size of 10 r_g. Only a corona orders of magnitude larger than typically measured for other AGNs would place Cen A in the physically allowed regime. However, the phenomenological nature of the cutoffpl model makes a physical interpretation difficult. A more realistic estimate of the temperature can be obtained using the thermal Comptonization compps model, which gives ${{kT}}_{e}={216}_{-22}^{+19}$ keV assuming a slab geometry and a seed photon temperature ${{kT}}_{{\mathtt{BB}}}=10\;{\rm{eV}}$. This temperature is stable against different geometries but depends on the seed photon temperature and spectral distribution. We find kT_e to be between 100 and 300 keV for input temperatures between 5 and 50 eV. Our results are consistent with the one measured by INTEGRAL for ${{kT}}_{{\mathtt{BB}}}=10\;{\rm{eV}}$ but statistically better constrained (${{kT}}_{e}=206\pm 62\;{\rm{keV}}$, Beckmann et al. 2011) and, assuming a slightly extended corona of $\sim 100\;{r}_{g}$, are in line with the pair-production limit.

The value of the folding energy of Cen A is discussed extensively in the literature, with no clear consensus. For example, Rothschild et al. (2006) measure a folding energy $\gt 1.5\;{\rm{MeV}}$ using RXTE while at a similar luminosity, Kinzer et al. (1995) find ${E}_{\mathrm{cut}}=254\pm 33\;{\rm{keV}}$ using CGRO/OSSE data. From the fluxes and spectral shape measured between 0.2 and 30 GeV with Fermi it is clear that the spectrum needs to roll over or break somewhere in the 100–1000 keV range (Abdo et al. 2010b).

It is interesting to note that nearly all well constrained measurements of a folding energy were performed by γ-ray instruments sensitive at energies $\gt 100\;{\rm{keV}}$, while purely X-ray missions often find very high lower limits of the folding energy far outside their covered energy range. As discussed above, this effect is likely connected to the difference between a cutoffpl and a realistic Comptonization model: the cutoffpl model is constantly curving, even far below the folding energy, while a realistic Compton spectrum is much more power-law-like at energies significantly below the temperature of the Comptonization plasma and rolls over more steeply than the cutoffpl above it (see Figure 3 in Fabian et al. 2015 and references therein). γ-ray instruments like INTEGRAL therefore detect the cutoff, but given their typically lower statistics at soft X-rays find an acceptable solution with a cutoffpl or a broken power-law model (Kinzer et al. 1995; Beckmann et al. 2011). For the X-ray instruments, on the other hand, the rollover is outside their energy range and they mainly measure the power-law part of the Comptonization spectrum, resulting in unconstrained or very high folding energies when using cutoffpl. By using a more physical Compton spectrum we obtain a statistically well constrained measurement and show that a temperature between 100 and 300 keV is in line with the observed spectra. We note that the seed photon spectrum in an advection-dominated accretion flow (ADAF) is not necessarily described by a multi-temperature blackbody spectrum. However, by sampling a wide range of input temperatures we demonstrate that the measured cutoff depends only weakly on the exact seed photon spectrum.

Despite the exceptional quality of the XMM-Newton and NuSTAR data, the origin of the hard X-rays cannot be uniquely determined. Both models are consistent with the broad-band spectral energy distribution (SED) presented by Abdo et al. (2010b). To better constrain which emission mechanism is dominant in Cen A modeling, a simultaneous SED is necessary which will be presented in a forthcoming work (C. Müller et al. 2016, in preparation). We rule out any contribution from reflection from the inner accretion disk with high significance, similar to the X-ray spectra of other radio galaxies. This measurement is in line with the idea that the hard X-ray emission from Cen A is dominated by SSC emission from the inner radio jet (Mushotzky et al. 1978; Abdo et al. 2010b). In this model the X-rays are produced in an outflowing plasma by Compton up-scattering synchrotron seed photons, and it explains well the broad-band SED other than the TeV γ-ray flux detected by H.E.S.S. (Aharonian et al. 2009; Abdo et al. 2010b).

Beckmann et al. (2011) remark, however, that a jet origin of the hard X-rays is more difficult to reconcile with the small long-term variability of the X-ray flux, which is more reminiscent of Seyfert galaxies. A possible solution includes contribution from both components, a thermal corona as well as a synchrotron jet (Soldi et al. 2014). Such a combined model has been proposed for other radio galaxies as well, such as 3C 120 (Lohfink et al. 2014) and 3C 273 (Grandi & Palumbo 2004; Madsen et al. 2015a). However, as Rothschild et al. (2006) and later Burke et al. (2014) found, the X-ray continuum shape is remarkably stable over time, despite significant flux changes. If the flux variability were induced by the inner jet component, we would expect some influence on the hard X-ray continuum. On the other hand, variability of the cutoff-energy as a function of flux has been observed with soft γ-ray instruments (e.g., with CGRO, Kinzer et al. 1995), following the "softer-when-brighter" correlation of Seyfert galaxies.

Some authors have reported a significant reflection fraction in Cen A (e.g., Fukazawa et al. 2011; Burke et al. 2014). If these detections are real, they do not seem to correlate with a particularly weak state of the X-ray flux, which we would expect if high fluxes correspond to a strong contribution from the jet emission, smearing out the reflection component. In particular, the INTEGRAL/SPI data used by Burke et al. (2014) are an average over 10 years, while Fukazawa et al. (2011) report a similar reflection fraction in both low and high flux states corresponding to a flux change of almost a factor of two. A mixture of standard thermal Comptonization and jet emission, in which the jet is driving the observed variability, thus seems unlikely.

If a stable accretion disk is present, we need to obscure it completely to eliminate all evidence of reflection from the observed spectrum. A puffed up accretion disk with a small corona could result in such an observed spectrum. However, Cen A is only accreting at $\lt 0.2\%$ of its Eddington luminosity, making a geometrically thick accretion disk unlikely (Paltani et al. 1998). Rather, the accretion disk might be strongly truncated and replaced with an optically thin accretion flow, as in the advection-dominated accretion flow (ADAF) model (Narayan & Yi 1995).

Rieger & Aharonian (2009) propose that Cen A is dominated by ADAF emission, which they use to predict that Cen A might be a source of TeV photons and ultra-high-energy (UHE) cosmic rays. While the latter claim is disputed in the literature (Petropoulou et al. 2014, who instead favor a two-zone SSC model,with UHE particles emerging from the lobes, but see also Khiali et al. 2015 for a model using magnetic reconnection to produce γ-rays), a large ADAF can explain the observed hard X-ray properties. Typical temperatures for the electrons in an ADAF Comptonization plasma are on the order of 100 keV, in good agreement with our measurement.

The fact that the NuSTAR spectrum is rather simple and well described by one power law or Comptonization component also argues against a mix of X-ray sources and would instead seem to favor a common origin for all observed hard X-rays.

The modified Chandra image shown in Figure 6 was used as input to the simulations and convolved with the respective NuSTAR and XMM-Newton PSFs. The extracted annuli were defined as regions with constant spectral properties, and each region was simulated into a separate image. When setting extraction regions for NuSTAR and XMM-Newton, we calculated the relative contributions of each image (or spectra) and folded the weighted input spectra through the response files and then combined them into the output spectrum for the requested region. These simulated spectra were then used as new background spectra for the NuSTAR and XMM-Newton data.

Because of the relatively modest extent of Cen A (≈100'') and the scale of the extraction regions (≈20''–40''), we made the following approximations to simplify the simulations: we assumed a flat effective area coinciding with the center of the object rather than a continuous extended effective area of the underlying diffuse component. This approximation is valid since most of the emission originates in the inner few arcseconds, dominating the response, and because at small off-axis angles ($\lt 2^{\prime}$) the extended effective area of a circular region cancels out the area obtained from the center of a circle. In addition we did not include an energy-dependent PSF, since the effect is typically on the order of a few arcseconds, while the scale size of our simulations was probing changes on a tens of arcseconds scale.

We use the emission as estimated from the Chandra data as background for the different XMM-Newton annuli and the NuSTAR spectrum. We then fit the XMM-Newton and NuSTAR data between 2–10 keV and 3–78 keV, respectively, with a partially covered power law and an iron line simultaneously, allowing for the normalization of the continuum and the $\mathrm{Fe}\;{\rm{K}}\alpha$ line to change.

This additional background changes the fit parameters significantly (e.g., the photon index softens from ${\rm{\Gamma }}=1.82$ to ${\rm{\Gamma }}\approx 1.95$), as the diffuse spectrum is very hard and we have no handle on a possible cutoff outside of Chandra's energy range. This fit is statistically similar, with ${\chi }_{\mathrm{red}}^{2}=2.13$ for 1739 dof. The reduced number of degrees of freedom is due to our binning to a certain S/N level, which requires stronger binning for the now higher background. Allowing for a high-energy cutoff by replacing the power law with the cutoffpl model did not improve the fit significantly (${\chi }_{\mathrm{red}}^{2}=2.02$ for 1738 dof) and gives a folding energy around ${E}_{\mathrm{fold}}\approx 150\;{\rm{keV}}$.

A better fit can be achieved by allowing the normalization of the background to vary (model recorn in XSPEC), individually for each XMM-Newton and NuSTAR spectrum (while requiring FPMA and FPMB and each annulus of MOS 1 and 2 to have the same scaling factor). This approach significantly improved the fit to ${\chi }_{\mathrm{red}}^{2}=1.62$ for 1730 dof. However, strong residuals in the NuSTAR data below 5 keV are still present. We therefore rule out a significant contribution from the diffuse emission to the low-energy end of the NuSTAR spectrum.

By ignoring all NuSTAR data below 5 keV and allowing for a free scaling of the background we obtain a very good fit with ${\chi }_{\mathrm{red}}^{2}=1.18$ for 1680 dof (model B). However, the scaling factors are very widely spread with ${\mathrm{CB}}_{\mathrm{FPMA}}=0.2$ and ${\mathrm{CB}}_{\mathrm{pn}1}=2.5$, where pn1 denotes the factor for the innermost pn annulus between 5'' and 15''. We give the best-fit parameters in Table 3.

When forcing the scaling factor for NuSTAR to be 1, i.e., assuming that our simulations capture exactly the correct background, we only find an acceptable fit when at the same time allowing for an exponential high-energy rollover (using the cutoffpl model in XSPEC). This model gives ${\chi }_{\mathrm{red}}^{2}=1.25$ for 1675 dof (model C). The best-fit parameters are shown in Table 3. Still the scaling factors for the background of the other instruments vary wildly, indicating that the diffuafse emission is not driving the observed differences.